Gömböc

A Gömböc is a convex, homogeneous, three-dimensional body that, when placed on a flat surface, always settles into a single stable and a single unstable equilibrium point. This means that if you place it in any random orientation, it will roll until it reaches its stable resting position, and then remain there. If nudged slightly, it will return to this position. The only other position it can rest in is an unstable equilibrium, where any tiny disturbance will cause it to roll away to the stable position.

The existence of such a shape was conjectured in the 1990s by Russian mathematicians Vladimir Arnold. It was proven mathematically and then physically realized in 2006 by Hungarian scientists Gábor Domokos and Péter Várkonyi. They used computer simulations to find the necessary mathematical conditions for a homogeneous body to have only two equilibrium points.

The first physical Gömböc was constructed by hand, and later, the process was mechanized. Gömböc is a Hungarian word meaning "roundish" or "spherical." The shape is not perfectly spherical, but rather a self-righting object. Its discovery has implications in fields such as physics, robotics, and even biology, as it provides a tangible example of a purely geometric property with practical applications. The unique property of having only two equilibrium points makes it a fascinating subject of study in geometry and mechanics.